- 2.8.1: In Exercises 14, find the given values of dy/dt and dx/dt. y dt x 1...
- 2.8.2: In Exercises 14, find the given values of dy/dt and dx/dt. x 1, 5 d...
- 2.8.3: In Exercises 14, find the given values of dy/dt and dx/dt. dy dt x ...
- 2.8.4: In Exercises 14, find the given values of dy/dt and dx/dt. x 4, y 3...
- 2.8.5: Area The radius of a circle is increasing at a rate of 2 inches per...
- 2.8.6: Volume The radius of a sphere is increasing at a rate of 2 inches p...
- 2.8.7: Area Let be the area of a circle of radius that is changing with re...
- 2.8.8: Volume Let be the volume of a sphere of radius that is changing wit...
- 2.8.9: Volume A spherical balloon is inflated with gas at a rate of 20 cub...
- 2.8.10: Volume The radius r of a right circular cone is increasing at a rat...
- 2.8.11: Cost, Revenue, and Profit A company that manufactures sport supplem...
- 2.8.12: Cost, Revenue, and Profit A company that manufactures pet toys calc...
- 2.8.13: Expanding Cube All edges of a cube are expanding at a rate of 3 cen...
- 2.8.14: Expanding Cube All edges of a cube are expanding at a rate of 3 cen...
- 2.8.15: Moving Point A point is moving along the graph of such that is 2 ce...
- 2.8.16: . Moving Point A point is moving along the graph of such that is 2 ...
- 2.8.17: Speed A 25-foot ladder is leaning against a house (see figure). The...
- 2.8.18: Speed A boat is pulled by a winch on a dock, and the winch is 12 fe...
- 2.8.19: Air Traffic Control An air traffic controller spots two airplanes a...
- 2.8.20: Speed An airplane flying at an altitude of 6 miles passes directly ...
- 2.8.21: Athletics A (square) baseball diamond has sides that are 90 feet lo...
- 2.8.22: Advertising Costs A retail sporting goods store estimates that week...
- 2.8.23: Environment An accident at an oil drilling platform is causing a ci...
- 2.8.24: Profit A company is increasing the production of a product at the r...
- 2.8.25: Sales The profit for a product is increasing at a rate of $6384 per...
- 2.8.26: Cost The annual cost (in millions of dollars) for a government agen...
Solutions for Chapter 2.8: Related Rates
Full solutions for Brief Calculus: An Applied Approach | 7th Edition
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
The two separate curves that make up a hyperbola
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.
An identity involving a trigonometric function of u - v
Difference of functions
(ƒ - g)(x) = ƒ(x) - g(x)
An equation written with exponents instead of logarithms.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
The domain of a function’s algebraic expression.
Real numbers shown to the left of the origin on a number line.
Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.
A graph of a polar equation or r = a cos nu.
Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,
Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)
Terminal side of an angle
A visualization of the Multiplication Principle of Probability.
See n factorial.